What is the Greatest Common Factor of 21735 and 21754?

Greatest common factor (GCF) of 21735 and 21754 is 1.

GCF(21735,21754) = 1

We will now calculate the prime factors of 21735 and 21754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21735 and 21754.

How to find the GCF of 21735 and 21754?

We will first find the prime factorization of 21735 and 21754. After we will calculate the factors of 21735 and 21754 and find the biggest common factor number .

Step-1: Prime Factorization of 21735

Prime factors of 21735 are 3, 5, 7, 23. Prime factorization of 21735 in exponential form is:

21735 = 3³ × 5¹ × 7¹ × 23¹

Step-2: Prime Factorization of 21754

Prime factors of 21754 are 2, 73, 149. Prime factorization of 21754 in exponential form is:

21754 = 2¹ × 73¹ × 149¹

Step-3: Factors of 21735

List of positive integer factors of 21735 that divides 21735 without a remainder.

1, 3, 5, 7, 9, 15, 21, 23, 27, 35, 45, 63, 69, 105, 115, 135, 161, 189, 207, 315, 345, 483, 621, 805, 945, 1035, 1449, 2415, 3105, 4347, 7245

Step-4: Factors of 21754

List of positive integer factors of 21754 that divides 21735 without a remainder.

1, 2, 73, 146, 149, 298, 10877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21735 and 21754. The biggest common factor number is the GCF number.
So the greatest common factor 21735 and 21754 is 1.

Also check out the Least Common Multiple of 21735 and 21754